He got a university degree in Physics at the University of Genoa (Italy) in 1962, and became full professor in Theoretical Physics at the same university in 1976.

His thesis and first scientific activity concerned experiments on the nuclear photo-effect. In 1964, mainly in collaboration with Giacomo Morpurgo, he started a theoretical study of the theory of Elementary Particle Physics in the light of Unitary Symmetry and Quark Models.

Starting from 1971 he undertook a systematic study of Renormalization Theory in the framework of Quantum Field Theory, considering in particular the problem of the renormalization of symmetries. He first attacked the study of the sigma model and of the associated current algebra anomalies, and then he moved to gauge theories, contributing to the discovery of the celebrated Becchi-Rouet-Stora-Tyutin (BRST) symmetry. The years after 1976 were devoted to the extension of renormalization techniques to various frameworks, including String Theory.

The 2009 Heineman Prize for Mathematical Physics has been awarded him for the discovery of the BRST symmetry.

Becchi chaired the Physics Department in Genoa University twice since 1983 and the Theory Scientific Committee of INFN from 1997 to 2003. He is Supervisory Editor of Nuclear Physics B since 1991, and editor of the Quantum and Statistical Field Theory section of Scholarpedia since 2008.